The present invention relates to digital signal processing, and more particularly to architectures and methods for oversampling quantization such as in analog-to-digital conversion.
Analog-to-digital converters (ADCs) are used to convert analog signals, such as music or voice, to digital format to allow for compression (e.g., MP3) and transmission over digital networks. An ADC samples an input analog signal (makes discrete in time) and quantizes the samples (makes discrete in amplitude) to give a sequence of digital words. For playback, a digital-to-analog converter (DAC) reconstructs (approximately) the input analog signal from the sequence of digital words. If the sampling rate of the ADC is higher than the Nyquist rate for the input analog signal, then the sampling is essentially reversible; whereas, the quantization always loses information. Thus ADC have a problem of optimal quantization.
A commonly used type of ADC includes oversampling plus a sigma-delta modulator; FIG. 3A illustrates one possible implementation of a one-stage modulator and quantizer. In particular, input signal x(t) is oversampled to give the input digital sequence x(nT) which will be quantized to give the output quantized digital sequence y(nT). The modulator operation includes subtracting a scaled and delayed quantization error, c e((n−1)T), from the input samples prior to quantization; this feedback provides integration of the overall quantization error. That is,y(nT)=Q(u(nT))e(nT)=y(nT)−u(nT)u(nT)=x(nT)−c e((n−1)T)Recursive substitution gives:e(nT)=y(nT)−x(nT)+c[y((n−1)T)−x((n−1)T)]++ . . . +ck[y((n−k)T)−x((n−k)T)]+See Boufounos and Oppenheim, Quantization Noise Shaping on Arbitrary Frame Expansion, Proc. ICASSP, vol. 4, pp. 205-208 (2005) which notes an optimal value for the scaling constant c as sin c(1/r) where r is the oversampling ratio.